There are a lot of questions here and it's hard for us to deal with so many questions! We get a large number of questions every day from our users and time simply does not allow us to spend so long on any one question. I've answered your first two questions below and given you a link to a page dealing with the topic where you can get more information. Please try to keep your questions succinct, however, and then we'll be able to answer them in full.

In your first example we would use an -ing form, though 'talk about' here is less likely than 'discuss':

There are some serious issues related to him that need to be discussed.

There are some serious issues related to him that need discussing.

Your second sentence is incorrect. First because we would not use 'speak' in this way (we would rather use 'say'), and second because it does not make sense even with the verb changed. 'You saying...' means more or less 'The fact that you said...' and so if we want to make a judgement about it then it needs to contain something questionable or controversial, such as an opinion, and 'eating food' is neither. We could say something like:

You saying eating food in the evening is unhealthy is not good.

The meaning here would be 'I don't approve of the fact that you said that eating food in the evening is unhealthy.' In these kinds of sentence we can use 'You saying...' or 'Your saying...', with no change in meaning.

When a verb is followed by another verb, often the second verb goes in the -ing or infinitive form, but the form of the verb doesn't really have anything to do with the meaning. In other words, the verb want is followed by an infinitive not because the infinitive means something different from the -ing form, but rather because that's the way the verb want is used in English. This is explained on our Verbs followed by ‘ing’ or by ‘to + infinitive’ 1 page.

The difficult thing is not 'verbs followed by a that-clause'… this is the normal case! Almost any verb can be followed by a that-clause (i.e. a clause with a verb that is conjugated). The special cases are when a verb cannot be followed by a that-clause, like 'want to do sth', 'want sb to do sth'. A list of those verbs would be very helpful! (In French, you say: 'Je veux que tu fasses quelque chose.'… the infinitive or gerund clause is not possible whereas in English, it is not only possible, as with 'before I did sth' or 'before doing sth', but it is compulsory.